Bayesian inference of transition matrices from incomplete graph data with a topological prior

Area of Science:

• Network science
• Graph theory
• Machine learning
• Statistical inference

Background:

• Network analysis relies on transition matrices from random walk models.
• Estimating these matrices from incomplete weighted graph data is challenging.
• Topological constraints offer valuable prior information for inference.

Purpose of the Study:

• To develop a data-efficient Bayesian method for inferring transition matrices.
• To leverage topological constraints alongside interaction data.
• To improve the accuracy of network analysis on incomplete datasets.

Main Methods:

• Developed an analytically tractable Bayesian approach.
• Integrated repeated interaction data with a topological prior.
• Compared the method against frequentist and Bayesian baselines on synthetic and real-world data.

Main Results:

• The proposed method significantly improves transition matrix inference accuracy, especially with limited data.
• The approach demonstrates robustness even with partial topological constraint knowledge.
• Higher accuracy in transition matrix estimation enhances downstream tasks like clustering and node ranking.

Conclusions:

• Integrating topological constraints with interaction data offers a powerful approach for network inference.
• The developed Bayesian method provides a reliable and data-efficient solution for incomplete network data.
• This work has practical implications for interdisciplinary data-driven analyses of networked systems.